Related papers: Asymptotic properties of generalized closed-form m…

Anomaly estimation, or the problem of finding a subset of a dataset that differs from the rest of the dataset, is a classic problem in machine learning and data mining. In both theoretical work and in applications, the anomaly is assumed to…

Objectives: Highly flexible nonparametric estimators have gained popularity in causal inference and epidemiology. Popular examples of such estimators include targeted maximum likelihood estimators (TMLE) and double machine learning (DML).…

Consider the problem of estimating a weighted average of the means of $n$ strata, based on a random sample with realized $K_i$ observations from stratum $i, \; i=1,...,n$. This task is non-trivial in cases where for a significant portion of…

We study approximate maximum likelihood estimators (MLEs) for the parameters of the widely used Heston stock and volatility stochastic differential equations (SDEs). We compute explicit closed form estimators maximizing the discretized…

When the spatial sample size is extremely large, which occurs in many environmental and ecological studies, operations on the large covariance matrix are a numerical challenge. Covariance tapering is a technique to alleviate the numerical…

We consider discrete default intensity based and logit type reduced form models for conditional default probabilities for corporate loans where we develop simple closed form approximations to the maximum likelihood estimator (MLE) when the…

This paper generalizes asymptotic properties obtained in the observation-driven times series models considered by \cite{dou:kou:mou:2013} in the sense that the conditional law of each observation is also permitted to depend on the…

Asymptotic efficiency of targeted maximum likelihood estimators (TMLE) of target features of the data distribution relies on a a second order remainder being asymptotically negligible. In previous work we proposed a nonparametric MLE termed…

In recent years, addressing the challenges posed by massive datasets has led researchers to explore aggregated data, particularly leveraging interval-valued data, akin to traditional symbolic data analysis. While much recent research, with…

Maximum regularized likelihood estimators (MRLEs) are arguably the most established class of estimators in high-dimensional statistics. In this paper, we derive guarantees for MRLEs in Kullback-Leibler divergence, a general measure of…

We describe Monte Carlo approximation to the maximum likelihood estimator in models with intractable norming constants and explanatory variables. We consider both sources of randomness (due to the initial sample and to Monte Carlo…

This paper studies the properties of debiased machine learning (DML) estimators under a novel asymptotic framework, offering insights for improving the performance of these estimators in applications. DML is an estimation method suited to…

Exact MLE for generalized linear mixed models (GLMMs) is a long-standing problem unsolved until today. The proposed research solves the problem. In this problem, the main difficulty is caused by intractable integrals in the likelihood…

Maximum likelihood is the most widely used statistical estimation technique. Recent work by the authors introduced a general methodology for the construction of estimators for functionals in parametric models, and demonstrated improvements…

In this paper we are interested in the Maximum Likelihood Estimator (MLE) of the vector parameter of an autoregressive process of order $p$ with regular stationary Gaussian noise. We exhibit the large sample asymptotical properties of the…

We present a general M-estimation framework for inference on the wavelet variance. This framework generalizes the results on the scale-wise properties of the standard estimator and extends them to deliver the joint asymptotic properties of…

With contemporary data sets becoming too large to analyze the data directly, various forms of aggregated data are becoming common. The original individual data are points, but after aggregation, the observations are interval-valued (e.g.).…

In this paper the Gaussian quasi maximum likelihood estimator (GQMLE) is generalized by applying a transform to the probability distribution of the data. The proposed estimator, called measure-transformed GQMLE (MT-GQMLE), minimizes the…

We advocate for a practical Maximum Likelihood Estimation (MLE) approach towards designing loss functions for regression and forecasting, as an alternative to the typical approach of direct empirical risk minimization on a specific target…

This paper develops a unified estimation framework, the Maximum Ideal Likelihood Estimation (MILE), for general parametric models with latent variables. Unlike traditional approaches relying on the marginal likelihood of the observed data,…